Question

question: 1
which equation describes a circle with center
$(4,-7)$ and radius 9?
a. $(x + 4)^{2}+(y - 7)^{2}=81$
b. $(x - 4)^{2}+(y + 7)^{2}=81$
c. $(x + 4)^{2}+(y - 7)^{2}=9$
d. $(x - 4)^{2}+(y + 7)^{2}=9$
question: 2
a lemon tart has a circular top with a radius of
5 inches. gina cuts a piece from the tart in the
shape of a sector formed by a central angle
with measure $27^{circ}$.
what is the area, in square inches, of the top of
the piece that gina cut out?
a. $a=\frac{27}{180}(25 pi)$
b. $a=\frac{27}{360}(10 pi)$
c. $a=\frac{27}{180}(10 pi)$
d. $a=\frac{27}{360}(25 pi)$

Explanation:

Question 1

Step1: Recall the standard form of a circle equation

The standard form of a circle equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Substitute the given values

Given center \((4,-7)\) (so \(h = 4,k=-7\)) and radius \(r = 9\). Then \(r^2=81\).
The equation becomes \((x - 4)^2+(y+7)^2=81\)

Question 2

Step1: Recall the area of a sector formula

The area of a sector \(A=\frac{\theta}{360}\times\pi r^2\), where \(\theta\) is the central angle and \(r\) is the radius.

Step2: Substitute the given values

Given \(\theta = 27^{\circ}\) and \(r = 5\) inches. Then \(r^2 = 25\).
The area formula becomes \(A=\frac{27}{360}(25\pi)\)

Answer:

Question 1: B. \((x - 4)^2+(y + 7)^2=81\)
Question 2: D. \(A=\frac{27}{360}(25\pi)\)